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I need to calculate the surface area of an oblate spheroid. My first step is to get the surface equation from Free-Form input. But I have trouble converting to a WM function and replace the focus point and the major axis radius coefficients with my values.

SurfaceData[Entity["Surface", "Spheroid"], "Image"]
SurfaceData[Entity["Surface", "Spheroid"], "SurfaceArea"]
sphOblated = Simplify[% /. x_String :> ToExpression[a, c]]
{a -> Sqrt[2], c -> 1}/%
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Perhaps a simpler method

SurfaceData[Entity["Surface", "Spheroid"], "SurfaceArea"][Sqrt[2],1]

which instantly returns

2*Pi*(2 + Sqrt[2]*ArcSinh[1])
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